*_What even is society... Let me know if you wanna see more of this series and if you've got specific video topic ideas, make sure to leave some comments down below too! :D_* Check out Brilliant to get a 30 day free trial of awesomeness! =D brilliant.org/FlammableMaths Check out my newest uploads over on @RockHardWoodDaddy ! =D ua-cam.com/video/uPLCnymscOE/v-deo.html My Merch! =D papaflammy.myteespring.co/ Support my channel and become a Patron! =) www.patreon.com/mathable ChatGPT Playlist: ua-cam.com/video/QoiWOF76Bkc/v-deo.html
can you get better results by doing it like this by taking two cases? 1. let x0, then solve by assuming e^x=x for example Am i right? I have no clue. I just saw the graph for e^x and started my own assumptions
Throwing it out there: GPT 3.5 is EXTREMELY bad at math. If you want to continue this series (and honestly have it do anything than very basic addition), shelling out 20$ for GPT-4 would increase the value of these videos by a lot. Love your content!
Also GPT 4 can now execute code, which adds all the computational power of python sci libs to the game, so if used to it's full potential it's actually not that bad. I use it as a study aid all the time.
The last one with the roots is completely solvable, just set the expression under the cbrt to (a+1)^3 and the expression under the sqrt to a^2 and solve for x. It's just a cubic polynomial!
For those curious what that looks like here's a little bit of it x-1 = a² x=a²+1 4x+9=(a+1)³ => 4a²+13 = (a+1)³ Expanding our and simplifying we get a³-a²+3a-12=0, I haven't found how to solve it algebraically but the cubic formula gives the same answer Wolfram does, just solve for a then x = a²+1 Keen readers will have noticed this method translates to all sums of 2 radicals, giving polynomials of degree equal to the highest root degree
@@soupisfornoobs4081 yeah I think cubic formula is the way to go here, here's how I did it: substitute u = a - 1/3 or a = u + 1/3 you wind up with: u^3 + (8/3)u - 299/27 = 0. i will use this version of the cubic formula: if u^3 + 3pu + 2q = 0, u = cbrt(-q + sqrt(q^2 + p^3)) + cbrt(-q - sqrt(q^2 + p^3)) some chugging through and simplifying later, this pops out: u = (1/3)(cbrt(299/2 + sqrt(91449)/2) + cbrt(299/2 - sqrt(91149)/2)) reverse both substitutions u -> a -> x. x = ((cbrt(299/2 + sqrt(91449)/2) + cbrt(299/2 - sqrt(91149)/2))/3 + 1/3)^2 + 1 which is roughly 5.70231. I ran newton's method on this and the results seem to agree. I did also run newton's method on the earlier [bullshit] transcendental question and I got the same result as wolfram.
I was going to type the same thing. My approach was to write 4 x + 9 = 4 (x-1) + 13 then set u = sqrt(x-1). Then a little algebra gives u^3 - u^2 + 3u -12 =0 which can be solved exactly.
I've heard that Khan Academy having been working with OpenAI to make a chat bot that is extremely more strict in answering math correctly, specifically so it can be used as a robot tutor. Might be cool to check that out if possible. Not sure if you'd have to ask them for access
i was inspired by this video to ask chatgpt for some integrals to solve, and when i asked it if i was right, in the process of solving, it claimed that 1+2/3-2/3=1-2/3=1/3
There is a way to get that last problem into a cubic which can then be solved to find an exact real solution. (4x+9)^(1/3)-sqrt(x-1)=1. Add sqrt(x-1) to both sides and cube both sides to get rid of the cube root. Expand the (1+sqrt(x-1))^3 on the right side to get 4x+9=1+3sqrt(x-1)+3(x-1)+(x-1)sqrt(x-1). factor sqrt(x-1) and expand 3(x-1) to get 4x+9=3x-2+(x+2)sqrt(x-1). Bring 3x-2 to the left side to get x+11=(x+2)sqrt(x-1). Square to get (x+11)^2=(x+2)^2(x-1). Expand to get x^2+22x+121=(x^2+4x+4)(x-1). Multiply out the right side to get x^2+22x+121=x^3+3x^2-4. Subtract the left side from the equation to finally get 0=x^3+2x^2-22x-125. The real solution to this cubic solves (4x+9)^1/3-sqrt(x-1)=1.
Finally, now not only can students solve homework with chatgpt, but teachers can assign it for students and them solving with chatgpt and so on....we gonna be so dumb 🤣🤣
bing AI was gaslighting and then kicking me out of the chat yesterday, just because it gave the wrong answer and I dared to ask it to calculate again...
For the exponential equation which you had to solve, you could have solved it by keeping e^x on one side and the rest of the stuff on the other side and then analyze their domain and range. Another way was to graph both lhs and rhs and finding the intersection points by hit and trial.
You can, since x/(-3x^4+1)*e^x=1 is equivalent to x/(-3x^4+1)*e^(x/(-3x^4+1))=1 you get the equation 3x^4+x-W(1)=0, solving for x (using wolfram) you get the correct solutions
I was expecting degree 6 polynomials, at least cubics are slightly better I wound up with u^3 - u^2 + 3u - 12 = 0 with x = u^2 + 1. Slightly different but eh Then cubic formula.
If you ask it more specific questions, like to give you some intégéral, then it's much nicer. would be great to see more videos like this in the area of human-computer interaction!
If you prove there aren't any integer solutions algebraically, you'll be halfway home to finding a real solution. What I mean is let 4x+9 = n^3, and x-1 = m^2, you can find a linear combination of those two such that x vanishes and use the fact that n-m = 1 to get a cubic polynomial you can show has no real solution. Solving that cubic polynomial and back subbing get you x, but it's not worth the effort.
I know Im late but for the last one can't you just move the square root bit to the other side, take to the power of 6 and yield a quadratic like equation after a lot of refactoring and squaring
I remember being very confused while living in Germany why they kept using something called the p q formel. I’m very pleased to learn it is just the quadratic formula for incels. Thanks, broseidon!
Are you from Germany or United States? Because you have a German accent but your country listed in your about page is the U.S just curious btw this was a great video!
you can write the equation in the form f(x)e^f(x) =g(x)e^g(x). and then solve f(x)=g(x). Depending on the functions you might yield more solutions than that, because xe^x isn't bijective, but we are engineers now, and we only care about solutions that have f(x)=g(x). Actually fuck me, the solutions have f(x)=/=g(x). I can't be bothered but if anyone knows a simple way of relating W_0(x) to W_-1(x), then you can solve the equation.
Chatgpt did my hw it’s got most of them wrong so I switched to a different ai and no I don’t let chatgpt do all my hw and I do understand the math problem I only use it check my answers
hello sir from India can you teach indefinite integral just like gn berman fiitjee module level application of derivatives 10+2 level definite integration probablity 10+2 level some manipulations in trigonometric equation 10+2 sl loney level
You didn't solve the last problem in the best possible way. You need to first isolate the cube root on the left side and then cube both sides, which leaves an 4x + 9 on the left side and (3x - 2) + (x + 2) sqrt(3x - 1) on the right side. Now isolate the term with the square root on the right by subtracting 3x - 2 from both sides, leaving you with x + 11 on the left side and (x + 2) sqrt(3x - 1) on the right side. Now squaring both sides removes all radicals, leaving you with polynomials on each side. Finally, by bringing all polynomials terms to one side, we obtain the cubic equation x^3 + 2x^2 - 22x - 125 = 0. As is the case with all cubic equations, this equation yields exact solutions involving radicals, one of which is real in this case. So ChatGPT gave you a very difficult problem to solve, but not an impossible one! On the other hand, the previous equation cannot be solved by elementary methods and needs to be numerically approximated, unless there's a special function I don't know about that it can be expressed in terms of, but I doubt this is the case.
6:30 I never understood about A HAS to be 1. I got A=3, B=5 and C=-2, put the numbers and got -2 and 1/3. What is the reason for making A=1? ~ 20 Σ {5R-20} R=0 I have started learning about Sigma, but this one has me stumped. I have been using [n(a₁ + aₙ)] ÷ 2 [20(-20+80)] ÷ 2 = 600 But when I enter my answer of 600, I get a . Where is my error?
*_What even is society... Let me know if you wanna see more of this series and if you've got specific video topic ideas, make sure to leave some comments down below too! :D_*
Check out Brilliant to get a 30 day free trial of awesomeness! =D brilliant.org/FlammableMaths
Check out my newest uploads over on @RockHardWoodDaddy ! =D
ua-cam.com/video/uPLCnymscOE/v-deo.html
My Merch! =D papaflammy.myteespring.co/
Support my channel and become a Patron! =) www.patreon.com/mathable
ChatGPT Playlist: ua-cam.com/video/QoiWOF76Bkc/v-deo.html
Glad to see you've made an awesome recovery :D
Flammable Maths
2:50 flammy reading an exclamation mark as factorial proves he is extremely based
I knew I wasn't the only one who noticed that.
I am proud of this community. We all came together and got Papa Flammy the equipment he needs.
Me too
yup it wasnt much but it was done through honest work.
I am late but why didn't he had 3-2-1 data back up?
2:51 hahaha only papa flammy could read "11!" as "eleven factorial"😂 love it
e^x is approx. 1, fucking legendary engineering
:D
applying the same zero order approximation to sin(x) you get that sin(x) = 0
can you get better results by doing it like this by taking two cases?
1. let x0, then solve by assuming e^x=x for example
Am i right? I have no clue. I just saw the graph for e^x and started my own assumptions
@@oni8337 x=0 is another useful zeroth order approximation
@@Smitology that's exactly what i just did
Throwing it out there: GPT 3.5 is EXTREMELY bad at math. If you want to continue this series (and honestly have it do anything than very basic addition), shelling out 20$ for GPT-4 would increase the value of these videos by a lot.
Love your content!
Will make sure to invest that small amount!
Tried it with GPT-4 and it gives much more interesting problems!
Even that sucks at math
It couldn't solve simple trigonometry for me. Yet when I asked it a fairly complicated numeric differential equation; it got it first try.
Also GPT 4 can now execute code, which adds all the computational power of python sci libs to the game, so if used to it's full potential it's actually not that bad. I use it as a study aid all the time.
let´s kick it up to eleven Factorial 💀
:D
Holy crap that’s a big boy
The last one with the roots is completely solvable, just set the expression under the cbrt to (a+1)^3 and the expression under the sqrt to a^2 and solve for x. It's just a cubic polynomial!
For those curious what that looks like here's a little bit of it
x-1 = a² x=a²+1
4x+9=(a+1)³ => 4a²+13 = (a+1)³
Expanding our and simplifying we get
a³-a²+3a-12=0, I haven't found how to solve it algebraically but the cubic formula gives the same answer Wolfram does, just solve for a then x = a²+1
Keen readers will have noticed this method translates to all sums of 2 radicals, giving polynomials of degree equal to the highest root degree
@@soupisfornoobs4081Thank you ! You just thought me a new trick
@@soupisfornoobs4081 yeah I think cubic formula is the way to go here, here's how I did it:
substitute u = a - 1/3 or a = u + 1/3
you wind up with:
u^3 + (8/3)u - 299/27 = 0.
i will use this version of the cubic formula:
if u^3 + 3pu + 2q = 0,
u = cbrt(-q + sqrt(q^2 + p^3)) + cbrt(-q - sqrt(q^2 + p^3))
some chugging through and simplifying later, this pops out:
u = (1/3)(cbrt(299/2 + sqrt(91449)/2) + cbrt(299/2 - sqrt(91149)/2))
reverse both substitutions u -> a -> x.
x = ((cbrt(299/2 + sqrt(91449)/2) + cbrt(299/2 - sqrt(91149)/2))/3 + 1/3)^2 + 1
which is roughly 5.70231. I ran newton's method on this and the results seem to agree.
I did also run newton's method on the earlier [bullshit] transcendental question and I got the same result as wolfram.
I was going to type the same thing. My approach was to write 4 x + 9 = 4 (x-1) + 13 then set u = sqrt(x-1). Then a little algebra gives u^3 - u^2 + 3u -12 =0 which can be solved exactly.
Nice. I put it into a cubic polynomial without using a’s. Ended up as,
x^3 + 2(x^2) - 22x - 125 = 0
11:00 lol 😂
I've heard that Khan Academy having been working with OpenAI to make a chat bot that is extremely more strict in answering math correctly, specifically so it can be used as a robot tutor. Might be cool to check that out if possible. Not sure if you'd have to ask them for access
sounds gorgeous, let me check this one out!
@@PapaFlammy69 I believe they call theirs Khanmigo.
GPT 4 with code execution is quite powerful as well.
When mathematicians finally agree that they too do approximations all the time.🤯🤯
Seeing you solve problems "live" is actually fun. And ChatGPT makes for funny moments!!
i was inspired by this video to ask chatgpt for some integrals to solve, and when i asked it if i was right, in the process of solving, it claimed that 1+2/3-2/3=1-2/3=1/3
xD
There is a way to get that last problem into a cubic which can then be solved to find an exact real solution. (4x+9)^(1/3)-sqrt(x-1)=1.
Add sqrt(x-1) to both sides and cube both sides to get rid of the cube root. Expand the (1+sqrt(x-1))^3 on the right side to get
4x+9=1+3sqrt(x-1)+3(x-1)+(x-1)sqrt(x-1). factor sqrt(x-1) and expand 3(x-1) to get 4x+9=3x-2+(x+2)sqrt(x-1). Bring 3x-2 to the left side to get
x+11=(x+2)sqrt(x-1). Square to get (x+11)^2=(x+2)^2(x-1). Expand to get x^2+22x+121=(x^2+4x+4)(x-1). Multiply out the right side to get x^2+22x+121=x^3+3x^2-4. Subtract the left side from the equation to finally get 0=x^3+2x^2-22x-125. The real solution to this cubic solves (4x+9)^1/3-sqrt(x-1)=1.
Finally, now not only can students solve homework with chatgpt, but teachers can assign it for students and them solving with chatgpt and so on....we gonna be so dumb 🤣🤣
11 factorial 😂 the sign of a true mathematician
Hilarious! I noticed the train. I recently got the crank operated wheel coaster with the steel balls. So much fun to build with my nephew
it is!!!
@PapaFlammy69 so cool I found it randomly in a hobby shop here in Toronto
0:11 made me laugh for 2 minutes😂😂😂
Papa: Chatgtp could I have something algebraic solvable?
Chatgtp: No! 😡
bing AI was gaslighting and then kicking me out of the chat yesterday, just because it gave the wrong answer and I dared to ask it to calculate again...
silly flammy, the ai knows once you bro, you never go
For the exponential equation which you had to solve, you could have solved it by keeping e^x on one side and the rest of the stuff on the other side and then analyze their domain and range. Another way was to graph both lhs and rhs and finding the intersection points by hit and trial.
Dude, because fo this video I understood chatgpt usefulness, love it
man is such a math guy when chat gpt put an exclamation point he said “11 factorial” 😂
I like how ChatGPT picked up on your badass lingo! That's rad to the max, dude!
Any chance we could see some more ,you laugh you math' with Dotson ?? 🙏🙏 loved that series
On the second equation you have x*e^x, can you just use the lambert double u function and are there any nice way to express W(x+y)?
You can, since x/(-3x^4+1)*e^x=1 is equivalent to x/(-3x^4+1)*e^(x/(-3x^4+1))=1 you get the equation 3x^4+x-W(1)=0, solving for x (using wolfram) you get the correct solutions
I've simplified the last question to be the cubic equation x^3+2x^2-22x-125=0, but it's still equally diabolic
sucks dick, ngl
I was expecting degree 6 polynomials, at least cubics are slightly better
I wound up with u^3 - u^2 + 3u - 12 = 0 with x = u^2 + 1. Slightly different but eh
Then cubic formula.
If you ask it more specific questions, like to give you some intégéral, then it's much nicer. would be great to see more videos like this in the area of human-computer interaction!
This was totally rad and bro-tastic!
I love how Papa Flammy also has a Razer mouse.
Today's flammable maths non-trivial trivia: 3 is not equal to zero.
The third problem could probably be solved by the lambert W function if you play with it enough
Veritasium made a great video on math duels! They used to be very popular among mathematics
If you prove there aren't any integer solutions algebraically, you'll be halfway home to finding a real solution. What I mean is let 4x+9 = n^3, and x-1 = m^2, you can find a linear combination of those two such that x vanishes and use the fact that n-m = 1 to get a cubic polynomial you can show has no real solution. Solving that cubic polynomial and back subbing get you x, but it's not worth the effort.
I meant no real int solution. If I recall n = 3.2685 or some shit
Pleeeassseeee tell me where you got those chalkboards
AI just generates something that looks like adequate speech, and that's just enough for normal humans.
Are there abnormal humans that we are not aware of 🤔
Me
Sigma man versus lambda AI. 😎
Great video and good luck!
how many levels of irony is GPT on?
You asked, the machine delivered
I really hope his students know he runs the greatest math channel on youtube (except for 3b1b)
They all do :p
Now, now, now ask ChatGPT what is 1+1 and it would give out a wrong answer
I think you should have told chat gpt to give a question that has rational solutions
ye, I realized that too later ^^'
what is that desk toy pendulum thing called
Swinging sticks
im curious what would happen jf you kept asking it for harder questions.
i'm not very experienced using newton's method, but maybe you could atleast approximate the solutions that way. not sure if that's possible though
sure, that would be possible! :)
I know Im late but for the last one can't you just move the square root bit to the other side, take to the power of 6 and yield a quadratic like equation after a lot of refactoring and squaring
awesome that we managed to collect the entire sum!
you bet!!!!!
"I don't believe that a lot of skaters are good at mathematics" is one of the stupidest thing I've heard from a smart person in a long time
I'm a skater and I like math, mathematician have rejected me... 😂
Ask for challenge to chatgpt 4
It gives ridiculously hard problems of integration
I wish you a lot of luck at the chiropractic.
20:05 press on exact form, there is a nice solution :cringe:
Hope no teacher figures this out for creating exams
I remember giving chatgpt a calc 2 exam once and it got like a low B
nice.
correction: you used chatgpt on your own calc 2 exam and got a low B.
6:31 i think you need to prove that
i mean, last time i checked -2 and 0 were different numbers
:^)
I’m sorry, but I cannot focus on your video- where did you get that twisty metal thing!!
Where did ChatGPT learn all the bro stuff haha
Elon Musk hasn’t confirmed that Andrew Dotson’s comment section wasn’t part of the training data
@@axelnils Elon Musk quitted OpenAI long before ChatGPT 3 became a thing.
@@axelnils What the fuk
Why didn't you use 'x= (-b ± sqrt(b² -4ac))/2 is it because it's easier to mess up?
just preference
I remember being very confused while living in Germany why they kept using something called the p q formel. I’m very pleased to learn it is just the quadratic formula for incels. Thanks, broseidon!
Are you from Germany or United States? Because you have a German accent but your country listed in your about page is the U.S just curious btw this was a great video!
Germany, gotta fix that ^^'
@@PapaFlammy69nice!
I'm disappointed that you didn't keep the bro mode at the max throughout the entire video
[Edit]
I mean the bro vibe was there but you toned it down
:^)
Mathematicians are not trained prompt engineers. No hard feelings.
Imagine not using the newton raphson method by hand 😒
ex dee
you can write the equation in the form f(x)e^f(x) =g(x)e^g(x). and then solve f(x)=g(x). Depending on the functions you might yield more solutions than that, because xe^x isn't bijective, but we are engineers now, and we only care about solutions that have f(x)=g(x).
Actually fuck me, the solutions have f(x)=/=g(x). I can't be bothered but if anyone knows a simple way of relating W_0(x) to W_-1(x), then you can solve the equation.
Chatgpt did my hw it’s got most of them wrong so I switched to a different ai and no I don’t let chatgpt do all my hw and I do understand the math problem I only use it check my answers
Try out bing for one too
Also the flammily is strong!
will note that! :)
U should see that thing try and do analysis proofs lmao
:'D
Engineering is approximating everything
wolframalpha yields a real solution with cubic roots
nice video
Bazinga.
Me just staring at the swinging sticks
Broseidon 😂😂
Hope you enjoy the xps :)
I do!!!
Would recommend GPT-4 with the Wolfram Alpha plugin and/or the Code Interpreter for some really interesting math features.
you know some dude has gone 140 kph on a skateboard. brosidon
:^)
Eleven factorial 💀
When you read the 11 ! As 11 factorial lol
Physicists: Estimating is key.
I love how you had to estimate due to lack of other alternate solution. I never would've considered such a simple skill
:)
lol this was hilarious
I literally guessed the answer to last on on the first try
hello sir from India
can you teach
indefinite integral just like
gn berman fiitjee module level
application of derivatives 10+2 level
definite integration
probablity 10+2 level
some manipulations in trigonometric equation 10+2 sl loney level
ChatGPT can't do math bro
I’m surprised I find this entertaining
2:50 did he just read "11!" as a factorial 🤡
sure thing :^) Is there any other meaning to ! besides factorial?
Waiting for asmr video
You didn't solve the last problem in the best possible way. You need to first isolate the cube root on the left side and then cube both sides, which leaves an 4x + 9 on the left side and (3x - 2) + (x + 2) sqrt(3x - 1) on the right side. Now isolate the term with the square root on the right by subtracting 3x - 2 from both sides, leaving you with x + 11 on the left side and (x + 2) sqrt(3x - 1) on the right side. Now squaring both sides removes all radicals, leaving you with polynomials on each side. Finally, by bringing all polynomials terms to one side, we obtain the cubic equation x^3 + 2x^2 - 22x - 125 = 0. As is the case with all cubic equations, this equation yields exact solutions involving radicals, one of which is real in this case. So ChatGPT gave you a very difficult problem to solve, but not an impossible one! On the other hand, the previous equation cannot be solved by elementary methods and needs to be numerically approximated, unless there's a special function I don't know about that it can be expressed in terms of, but I doubt this is the case.
I'm disappointed of him . This way to solve is obvious. Why he didn't use it😢
@@Jimmy-vg2gd Don't know. I guess it just didn't occur to him when he made the video. He should redo this one!
What bullshit
second comment
That series gonna be cool asf
6:30 I never understood about A HAS to be 1. I got A=3, B=5 and C=-2, put the numbers and got -2 and 1/3. What is the reason for making A=1? ~
20
Σ {5R-20}
R=0
I have started learning about Sigma, but this one has me stumped.
I have been using [n(a₁ + aₙ)] ÷ 2
[20(-20+80)] ÷ 2 = 600
But when I enter my answer of 600, I get a .
Where is my error?
gigachad ChatGPT